I heard from the great and wise Rabbi Uziel Milevsky ztz"l in a shiur which
explained this issue. If you notice over there it says that even after
Rivka had offered the water for Eliezer and the camels yet still Eliezer
studied the camel drinking and it says that he then waited to see if Hashem
had made his ways successful or not. Then when they drank and continued
drinking that he gave Rivka the jewelery and then spoke to her. The order
of events is difficult. If she has done as he stipulated in his requested
sign(to offer he and the camels water) why did he continue to wait and see.
While he may have had trepidation until he heard her family background he
did still gave her the jewelery before he knew of the family background.
Further(Breisheis 24:1-27) Eliezer's giving of the jewelery is immediately
preceded by not the beginning of their drinking but the end of their
drinking. Explanation: Indeed Avrohom's camel's (like Rav Pinchas ben
Yaer's donkey) wouldn't take from what is stolen. This sensitivity was so
high that if Rivka had not sincerely wanted to give of her water but merely
offered it due to social pressure or marital possibility biases then the
camels would've regarded that thievery. However, this sensitivity in the
righteous' animals only sets in after the basic life imbuing thirsts are
quenched. Camels have two distinct types of drinking, replenishing their
life fluids and adding excess storage to their humps. Thus, when the camels
drank beyond life sustaining levels and completed a hump storage drink that
proved that there was no thievery involved. I hope this is found helpful
and inspiring.
Yerachmiel Landy